POEMS: Product of Experts for Interpretable Multi-omic Integration using Sparse Decoding

TL;DR

POEMS addresses the interpretability–nonlinearity trade-off in unsupervised multi-omics integration by combining sparse feature-to-factor mappings with a Product-of-Experts fusion of modality-specific posteriors into a shared latent space. A gating network estimates per-omic contributions, while a Spike-and-Slab prior enforces sparse, biomarker-friendly loadings and a vectorized SparseVAE decoder enables scalable reconstruction. Empirical results on BRCA and KIRC TCGA data with mRNA, DNA methylation, and miRNA demonstrate competitive cancer subtyping performance alongside biologically meaningful, cross-omic biomarker associations and subtype structure. Overall, POEMS shows that interpretability and predictive power can co-exist in deep multi-omics models, with practical implications for biomarker discovery and cross-omic insight.

Abstract

Integrating different molecular layers, i.e., multiomics data, is crucial for unraveling the complexity of diseases; yet, most deep generative models either prioritize predictive performance at the expense of interpretability or enforce interpretability by linearizing the decoder, thereby weakening the network's nonlinear expressiveness. To overcome this tradeoff, we introduce POEMS: Product Of Experts for Interpretable Multiomics Integration using Sparse Decoding, an unsupervised probabilistic framework that preserves predictive performance while providing interpretability. POEMS provides interpretability without linearizing any part of the network by 1) mapping features to latent factors using sparse connections, which directly translates to biomarker discovery, 2) allowing for cross-omic associations through a shared latent space using product of experts model, and 3) reporting contributions of each omic by a gating network that adaptively computes their influence in the representation learning. Additionally, we present an efficient sparse decoder. In a cancer subtyping case study, POEMS achieves competitive clustering and classification performance while offering our novel set of interpretations, demonstrating that biomarker based insight and predictive accuracy can coexist in multiomics representation learning.

Figures (9)

• Figure 1: Schematic overview of POEMS. Each omics, $\mathbf{x}^i$, is encoded into a Gaussian posterior with mean $\boldsymbol{\mu}_i$ and variance $\boldsymbol{\sigma}_i^2$. The posteriors are fused via a Product-of-Experts, with gating weights $\boldsymbol{\alpha}_v$ controlling each omic’s contribution to the shared latent $\mathbf{z}$. Before reconstruction, $\mathbf{z}$ is modulated by the sparse feature-to-factor matrix $\mathbf{W} \in \mathbb{R}^{D \times K}$, ensuring each feature depends on a limited subset of latent dimensions. These masked versions are then passed through modality-specific decoders for reconstruction. The yellow highlight shows the interpretable link between the 4th feature of $\mathbf{x}^1$ and the 2nd latent factor, $\mathbf{W}_1^{4,2}$.
• Figure 2: Top 10 activated features per omic, showing modality-specific feature-to-factor associations.
• Figure 3: Subtype correlation maps with respect to input features and latent factors.
• Figure 4: Per-sample gating weights ($\alpha$) indicating each omic’s contribution.
• Figure 5: Aggregated activation strengths of the top 10 features across mRNA, DNAMeth, and miRNA modalities, derived from each omic’s feature–factor mapping matrix $\mathbf{W}$. For each feature, the aggregated strength is computed as the sum of absolute loading values across all latent dimensions in $\mathbf{W}$. The x-axis labels are the original omic feature names.